B.3.1—Pressure

Pressure

Pressure is perpendicular force distributed over area:

$P=\frac{F_{\perp}}{A}$

Its SI unit is the pascal, $1\,\mathrm{Pa}=1\,\mathrm{N\,m^{-2}}$ .

Use the normal component

Only the component of force perpendicular to the surface contributes to pressure on that surface. A tangential component produces shear rather than normal pressure.

Read the proportionality

At fixed force, doubling area halves pressure. At fixed area, doubling the perpendicular force doubles pressure. Pressure is a scalar even though the force producing it has direction.

Worked example from the mapped local textbook

A $51\,\mathrm{kg}$ student stands on one foot with contact area $62\,\mathrm{cm^2}=62\times10^{-4}\,\mathrm{m^2}$ . The perpendicular force is the weight, $F=mg=(51)(9.8)=5.0\times10^2\,\mathrm{N}$ .

$P=\frac{F}{A}=\frac{5.0\times10^2}{62\times10^{-4}}=8.1\times10^4\,\mathrm{Pa}$

The result is large because the same weight acts over a small area.

Common trap

Do not use total force if the force is angled. Resolve it perpendicular to the surface first, and keep area in square metres.

How it is assessed

The evidence includes a units-concept multiple choice and a structured force/area calculation with an angled force.

Command terms

State / Estimate / Determine

What earns marks

Use pressure as perpendicular force per unit area: P=F⊥/A. Resolve any angled force before calculating, use area in m², and state Pa or N m⁻². For energy-density questions, recognize that pressure has the same units as energy per volume.

Watch for

Using total angled force rather than its perpendicular component or reporting force units instead of pascals.

Representative question

[Maximum number: 3]

Estimate the maximum safe mass that this arrangement can hold.

$\begin{aligned} \mathrm{F}=4 P A=4\left(1.6 \times 10^{5}\right)(15 \times 24 \times 1.8)=4.14 \times 10^{8} \mathrm{~N} \mathrm{F}=m g \cos \theta=\mathrm{m}(9.8)(\cos 4)=9.78 \mathrm{~m} \mathrm{~N} m=\frac{4 P A}{g \cos \theta}=\frac{4.14 \times 10^{8}}{9.78}=4.3 \times 10^{7} \mathrm{~kg} \end{aligned}$

Do not award MP2 if the cos θterm is omitted.

Allow ECF for MP3.

Macroscopic equations

Pressure is $P=F_{\perp}/A$ . For a fixed amount of gas, empirical laws combine to $PV/T=\text{constant}$ , and the ideal-gas equations are $PV=nRT=Nk_BT$ .

Microscopic model

Particles move randomly and collide elastically with walls. Momentum transfer produces pressure, with $P=\frac13\rho\overline{v^2}$ . For a monatomic ideal gas, $U=\frac32Nk_BT=\frac32nRT$ .

Bridge the descriptions

Use $n=N/N_A$ to move between moles and particles. Choose the equation from the data provided, convert temperature to kelvin, and keep SI units consistent.

Model boundary

The ideal approximation works best at high temperature and low pressure or density. At high density, high pressure or near condensation, finite particle size and intermolecular forces matter.

B.3.1—Pressure

Calculate Pressure from Normal Force

B.3.1 Exam Analysis

Assessment in practice

Synthesize B.3 Gas Laws

Question 1